Monopsony
A monopsony is a market characterized by a single buyer. As a single buyer of labor, labor
market monopsonist faces an upsloping supply of labor. In symbols, we could write w = w(L) where w is
the wage, L is the number of workers hired, and the condition w’(L) > 0 reflects the firm’s monopsony
power: additional labor can be acquired only by increasing the wage.
The firm’s labor cost is the wage times the number of workers hired: C(L) = w(L)∙L. To find the
firm’s marginal resource cost, MRC, we differentiate C(L) with respect to L. Using the product rule,
MRCL = w(L) + Lw’(L). Since w’(L) > 0, this proves the proposition stated in the text: MRCL > w, the
firm’s marginal resource cost exceeds the wage rate.
Note that the MRC is the sum of two terms, the wage rate and Lw’(L). What is the second term?
w’(L) is the increase in the wage rate required to obtain one more worker and L is the number of workers
hired. Consequently, we can think of Lw’(L) as the total cost of increasing each current worker’s wage up
to the level required to bring in the marginal worker.
Of course, this modification in the firm’s market power requires that we revisit the earlier rules
for the least-cost and profit-maximizing combinations of labor and capital from the previous chapter. In
the interest of generality, suppose the firm has monopsony power in its purchase of capital as well, so that
r = r(K) and r’(K) > 0. In a manner analogous to the marginal resource cost of labor, we find that the
firm’s marginal resource cost of capital is given by MRPK = r(K) + Kr’(K). Under these conditions, the
firm’s profit is given by π(L, K) = Pg(L, K) – (w(L)L + r(K)K), where P is the market price of the firm’s
output, and g(L, K) is the firm’s production relationship. Differentiating profit with respect to both L and
K, we obtain the first-order conditions:
∂g
∂π
=P
– (w(L) + Lw’(L)) = P∙MPL – MRCL = MRPL – MRCL = 0
∂L
∂L
∂π
∂g
=P
– (r(K) + Kr’(K)) = P·MPK – MRCK = MRPK – MRCK = 0
∂K
∂K
A simple rearranging of these terms gives the two conditions noted in the footnote of the text:
Cost minimization requires equality of each input’s ratio of marginal product to marginal resource cost,
while profit maximization requires equality of each input’s ratio of marginal revenue product to marginal
resource cost, and that this ratio equals 1.